Massive Complexity

Scholars used to marvel at the elegance and mathematical simplicity of the universe. That was before we invented supercomputers.

Simulation of the ejected matter from colliding neutron stars. Credit: NASA

From the days of Newton and Galileo to the middle of the 20th century, science was a mixture of brilliant insight and trial-and-error. Intelligent, learned people would come up with ideas and build experiments to test them. It was a golden age, romanticized by the iconic ideas of the scholar in their study and the tinkerer in their garage, creating new machines and discovering new laws of nature.

In the process, better tools were built. Instruments were invented that were more precise, and could measure more things. A new field of mathematics opened up, statistics, which gave scientists guidance on how to make hypotheses, devise experiments, and interpret data. Then, computers came upon the scene, able to deal with vastly more data than human beings could.

When computers and statistics advanced to the point at the end of the 20th century that the supercomputer was invented, science changed. No longer was it dominated by eccentric individuals writing equations on chalkboards and napkins. Instead, science entered the era of big data, when computers gained the ability to store and analyze billions of data points at once. The change was so dramatic that it would be fitting to say we are in a new era of science, which we might call Phase-II science. Whereas during Phase-I science we could learn about the elegant and simple parts of nature, the tools of Phase-II science let us take a peek into its messiness and complexity.

What makes a system complex? One factor is the number of degrees of freedom it has. Degrees of freedom are ways that a system can change. A lever has one degree of freedom; it can be pulled or pushed. A pencil has six degrees of freedom; it can move in three dimensions, and spin along three axes. Another contributor to complexity is how interconnected the parts of the system are. And another contributor to complexity is how many environmental factors come into play, and how unpredictable they are. There are many more as well.

One type of complex system is a chaotic system. Chaotic systems require exponentially more precision the longer you want to accurately model it. The classic example is the three-body problem, where three stars of similar mass are orbiting each other. The stars will swing around each other wildly and erratically, and even a small change in the initial conditions will lead to drastically different paths.

Another type of complex system is a holistic system. In a holistic system, all of the parts are interconnected in such a way that a change in one part causes changes throughout the entire system. DNA is a holistic system, because a change in a single nucleotide can affect an entire gene, and a change in a single gene can affect the entire body. Brains are holistic systems, because a change in one neural pathway can affect quite a lot about a person’s cognition or memory or other mental processes.

Supercomputers can model some chaotic and holistic systems, and are getting better all the time. But there is one more kind of complex system, which I call massively complex, which not even supercomputers can model accurately. Massively complex systems are complex systems which function in environments that are also complex. Human behavior is a massively complex system, because humans are already complex, and we interact with all manner of unpredictability in our environments every day. Economics and sociology are massively complex, because they are holistic, and they happen in a very large and unpredictable environment.

It is anyone's guess as to whether we will ever be able to model and understand massively complex systems. Maybe we won't, because it is just too complicated. But people might have made that argument about normally complex systems before supercomputers were invented, so we shouldn't be so hasty. Maybe our supercomputers will keep improving until they can model massively complex systems as well as they do normally complex systems today. Or maybe it will require another revolution in computing technology, like quantum computers, ushering in a new era of Phase-III science. Only time will tell, and I am quite excited to see what the future brings.